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arXiv · 2406.08388

Topological linear response of hyperbolic Chern insulators

Canon Sun·Anffany Chen·Tomáš Bzdušek·Joseph Maciejko
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Abstract

We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing the Kubo formula to hyperbolic lattices, we show that the Hall conductivity is quantized to $-e^2C_{ij}/h$, where $C_{ij}$ is the first Chern number. Through a flux-threading argument, we provide an interpretation of the Chern number as a topological invariant in hyperbolic band theory. We demonstrate that, although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states, resulting in a tremendous simplification of the topological band theory. Finally, we verify our results numerically by computing various Chern numbers in the hyperbolic Haldane model.

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Canon Sun, Anffany Chen, Tomáš Bzdušek, Joseph Maciejko. 2024-06-12. Topological linear response of hyperbolic Chern insulators. https://doi.org/10.21468/scipostphys.17.5.124

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